The work is directed along essentially two parallel routes. One is to extend or to reformulate the several rigorous and numerically successful statistical mechanical theories of simple electrolyte solutions in order that they be applicable to the more complex systems of biophysical interest, such as polyelectrolytes and membranes, thus providing reliable theoretical calculations of the electrostatic and thermodynamic properties of such systems. The other route is to apply calculations of the balance between the repulsive electrostatic forces and the van der Waals attractive forces to polyelectrolyte systems.